The prime at infinity and the rank of the class group in global function fields

In this paper we construct, for any integers m and n, and 2⩽g⩽m-1, infinitely many function fields K of degree m over F(T) such that the prime at infinity splits into exactly g primes in K and the ideal class group of K contains a subgroup isomorphic to (Z/nZ)m-g. This extends previous results of the author and Lee for the cases g=1 and g=m.